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Simplifying q2 + -4q + -15 = 81 Reorder the terms: -15 + -4q + q2 = 81 Solving -15 + -4q + q2 = 81 Solving for variable 'q'. Reorder the terms: -15 + -81 + -4q + q2 = 81 + -81 Combine like terms: -15 + -81 = -96 -96 + -4q + q2 = 81 + -81 Combine like terms: 81 + -81 = 0 -96 + -4q + q2 = 0 Factor a trinomial. (-8 + -1q)(12 + -1q) = 0Subproblem 1
Set the factor '(-8 + -1q)' equal to zero and attempt to solve: Simplifying -8 + -1q = 0 Solving -8 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1q = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1q = 0 + 8 -1q = 0 + 8 Combine like terms: 0 + 8 = 8 -1q = 8 Divide each side by '-1'. q = -8 Simplifying q = -8Subproblem 2
Set the factor '(12 + -1q)' equal to zero and attempt to solve: Simplifying 12 + -1q = 0 Solving 12 + -1q = 0 Move all terms containing q to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1q = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1q = 0 + -12 -1q = 0 + -12 Combine like terms: 0 + -12 = -12 -1q = -12 Divide each side by '-1'. q = 12 Simplifying q = 12Solution
q = {-8, 12}
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